Very interesting thread.
I'd like to add a couple of points, from the POV of a pracitioner and student of Vedic religion. I don't read Sanskrit, but am familiar with many Sanskrit terms due to many years of study. Also have practiced Hatha Yoga for years, as well as Bhakti Yoga. And the two have little in common, except regarding some basic understandings of spiritual identity.
Some points for your consideration:
1. Hinduism is essentially monotheistic. There are two branches (naturally many sub-branches, but two main branches) - monism and dualism. Monism (called Mayavada) holds that there is no eternal God who is a Person, that God is an formless void of light, and therefore each individual is also not an eternal soul, but a particle of the formless God. This branch has historically, until recent times, been the minor branch. The other branch, dualism (or Vaishnavism), holds that God is one, the Supreme Person, and that all creatures are in actual essence eternal, individual souls, part of God the way children are part of the parent, but eternally individual.
2. The Vedic scriptures state unequivocally that God is one, that the devas or demigods are not Godhead, but merely empowered servants for maintaining the functions of the manifested created universe. God has His Kingdom beyond the materially created universes. If you read the Puranas, you will see that even Shiva and Brahma - two of the most powerful devas - worship God Himself, and consider themselves His servants. So Hinduism in essence is not polytheistic. Many Hindus are not clear about this, just as many who call themselves Christian are not clear about their foundational teachings.
3. The Vedas predate not only Christianity but also Greek, Roman, and Egyptian civilizations. When the British conquered India, various British and European Indologists did their best to convince themselves and others that the Vedas were of recent origin. Some of this was done as a conscious subtrefuge. But the Vedas themselves state that their written origin was 5,000 years ago; and in fact, Buddha's appearance as well as Jesus Christ's are predicted in at least two Puranas that I know of.
Personallly speaking, real prayer is meditative, and real meditation is prayerful.
I should also add that in the Vedas, God is considered to have unlimited names. The Mahabharata has a chapter (or section) entitled "The Thousand Names of Vishnu" - "Vishnu Sahasranama". And those names are not considered all-inclusive by any means.
Meditation on the holy names of God - including meditation silently, out loud, with beads, as part of prayers, or even with singing - are all traditional methods of Hindu meditation.
Interestingly, there are 81 references in Psalms to the holy name of God that I have found, and the name's potency to give protection.
You will, I hope observe, that nowhere did I indict Hinduism for polytheism. As an Orthodox Christian, I view the fundamental defect of paganism as the confounding of the created with the Uncreated.
I am fond of pointing out to atheists that theism is not one-god-paganism, by which I mean that the radically transcendant God is in no way like any created thing, whereas the gods of paganism (and even God as misconceived by some materialistically-minded Christians) are very much like created things.
Since you are a devote of Vedic religion, we must simply agree to disagree, but doubtless just as I find something defective in the temporal eternity of cyclic Hindu cosmology, you see something wrong with the atemporal eternity Christians attribute to the Uncreated God.